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3hati and 5hatj are vector along x-axi...

`3hati and 5hatj` are vector along x-axis and y-axis respectively. Find the resultant vector

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Consider two particles A and B moving along the X-axis with uniform velocity `v_(A) and v _(B).`
Let `x_(OA) and x_(OB)` be their displacemetn from the origin O at `t=0.`
If `x_(A) and x_(B)` arfe tieir position co-ordinates then at `t=t,`
`therefore x_(A) =x_(OA) +v_(A)t`
`x_(B) =x_(OB) +v_(B)t`
At `t=t` the displacement of particle B with respect to particle A,
`x_(B) -x_(A) =(x_(OB) -x_(OA)) (v_(B)-v_(A))t`
where `x_(OB)-x_(OA)` =displacement of particle B with respect to particle A at t =0 and `v_(B) - v _(A)=v _(BA)` is the relative velocity of B with respect to particle A.

When `v _(A) = v_(B)` then from equation `x _(B) - x _(A) = x _(OB)- x _(OA)` this means that the distance between two particles will remain equal to initial distance at any instant of time.

If `v_(A) gt v _(B)` both teh particles will meet at time t at this instant their relative displacment will be` x_(B) - x_(A) =0.`These after particle A overtakes particle B at this time.
If `v_(B) gt v_(A)` then the relative displacment `x_(B) -x_(A)` of both the particles will increase with time. Therefore they will never meetn on their path.

If the velocities of two trains moving in mutually opposite directions are `v_(A) and v _(B)` respectively, then
`v _(AB) =- v_(BA)`
Let, train A is moving in positive direction and train B is moving in negative direction, then
`v _(A) =+ v _(A) and v _(B) =- v _(B)`
`v _(AB) = v _(A) -v_(B)` `= v _(A) - (-v_(B))`
`=v_(A) + v_(B)`
and `v_(BA) =v_(B) -v_(A)`
`=- v_(B) -v_(A)`
` =- (v_(A) + v _(B))`
Hence, the relative velocity is greater than individual velocities of the trains.
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